Dilation and particle breakage effects on the shear

Introduction

Low hardness, porous grains and different originof calcareous soils results to different shearbehavior compared with siliceous soils especiallyagainst driving piles. Usually laboratory testsshow high shear strength for calcareous sands.However, these sands have shown someproblems during constructions and pile drivings. Different origins and different depositionconditions creates calcareous soils havingdifferent characteristics. Information about thesesoils such as density, stress history, dimension,shape and strength of grains are very limited.

Investigations of Jewell and Andrews (1988),Coop and Lee (1993), Jewell and Khorshid(1988), Kaggwa (1998), Coop (1990), Airey andFahey (1991), Hyodo et all (1998), Al-Shafei(1999), Salehzadeh (2000), Ismail et all (2002),Luzzani and Coop (2002), Coop et all (2004) andSharma et all (2006) are some examples ofconducted studies on calcareous soils.

Perhaps, Chandler presented the most completeidea about calcareous sands having crushable

grains in 1985 that improved by Baharom andStalleberass in 1998. They told that critical statein sands having crushable grains in triaxial testsis in fact equilibrium between contractions due toparticles breakage and dilation resulted fromrearrangement of grains. The question is, ifcontraction due to particle breakage and dilationresulted from particles rearrangement is not equaland balanced, how is the critical state? When theparticles breakage is ceased? Luzzani and Coop(2002) and Coop et all (2004) conducted somering shear tests up to very large shear strains andpresented that particles breakage is continued bycontinuing the shear strains to very large strains.They verified that critical state in triaxial tests isin fact a balance between volume reduction dueto particles breakage and dilation resulted fromparticles rearrangement. This is a transient statesince stable grading is not reached.

In this paper monotonic shear behavior of twocalcareous sands having different physicalproperties are investigated using consolidated-drained and consolidated- undrained triaxialtests. The studied calcareous sands are obtainedfrom two different regions of Persian Gulf and

108 International Journal of Civil Engineerng. Vol. 6, No. 2, June 2008

Dilation and particle breakage effects on the shear strength of calcareous sandsbased on energy aspects

Mahmoud Hassanlourad1, Hosein Salehzadeh2, Habib Shahnazari21Ph.D Candidate, Iran University of Science and Technology and Islamic Azad University- Zanjan Branch

2Assistant Professor, Collage of Civil Engineering, Iran University of Science and Technology

Abstract: In this paper shear behavior of two calcareous sands having different physical properties areinvestigated using drained and undrained triaxial tests. The investigated sands are obtained from two differentzones located in Persian Gulf, Kish Island and Tonbak region. Analysis based on energy aspects show thatfriction angle in these soils, having crushable particles, is formed of three components: substantial internalfriction angle, dilation and particle breakage angle. Dilation component is available in the two investigatedsand. Particle breakage component is a function of grains hardness, structure and geometry shape. Particlesbreakage decreases the volume of sample during drained tests and creates positive pore water pressure duringundrained tests. Two investigated sands show different amount of dilation and particle breakage under similarconditions. Simultaneous dilation and particles crushing and different amount of them result in different shearbehavior of the two studied sands. Energy aspects are used to determine the effect of particle crushing on theshear strength. There is a suitable compatibility between relative breakage of grains and consumed energyratio for particle breakage.

Key Words: calcareous soil, triaxial test, dilation, particle breakage, energy

south of Iran.

At first, the results of consolidated-drainedtriaxial tests on two sands are analyzed usingRow theory and its improved version by Chen etall (2000). Test results show that two calcareoussands having crushable grains have somedifferences and some similar features. In thesesands, shear strength and then internal frictionangle has formed from three components:substantial internal friction, dilation and particlebreakage during shearing. Dilation and breakagefriction angle is a function of initial relativedensity, initial confining pressure, initial grading,texture and hardness of sand particles. Based ontest results, dilation and particles breakage aredifferent for two investigated calcareous sands.Like CD tests, the CU tests show somedifferences and similar features like pore waterpressure development and then shear strength ofsamples for the two studied sands.

Materials

As mentioned before, two calcareous sands arestudied in this paper. Kish Island sand, obtainedfrom east of Kish Island, located in Persian Gulfin the south of Iran and Tonbak sand obtainedfrom depth of 2 to 9m of sea bed where the depthof water equals 10m, located in Persian Gulf andsouth of Iran. Particle size distribution of the twosands is shown in figure 1. According to thisfigure, Kish Island sand is somehow finer thanTonbak sand. Electronic microscopic pictures

(SEM) of the two sands are shown in figure 2.According to this figure, the two sands havedifferent textures. Kish Island sand grains arebiological and have porous structure with bulkyand subangular shape. However Tonbak sandgrains are porous, angular, weaker and some ofthem are platy and with thin walls. It seams thatTonbak sand grains are more fragile than KishIsland grains. Then it’s may be the volumereduction due to particles breakage in Tonbaksand during loading is more than Kish Islandsand. Physical properties of the two sands aresummarized in table 1. It’s expected that twosand, have different shear behavior regarding totheir different grains texture and physicalproperties.

Sample Preparation and Tests

For sample preparation, at first some determinedsand (oven dried) is poured into a membraneinside the triaxial apparatus mold of sample.Then, the determined sand is placed inside themold by uniform tamping to the mold. Then asample with specific relative density is created.The prepared samples have 38mm diameter and76mm height. After sample preparation, a lownegative pressure as much as 10kPa is applied tothe sample and the mold is removed. Afterputting the sample inside of the triaxial cell, asmall confining cell pressure as much as 20kPa isapplied to the sample. For saturation of thesample, at first CO2 gas is passed through thesample for about 10 to 15minutes, then the de-

109Mahmoud Hassanlourad, Hosein Salehzadeh, Habib Shahnazari

Fig.1 Particle size distribution of the studied sands.

aired water is passed through the sample. In allprocesses a confining effective pressure of about10kPa is kipped. Using a back-pressure andkeeping a confining effective pressure of about10kPa, when the air bubbles are solved inside thepore water and the B value is 0.95, the sample issaturated. According to the described method, alltests are prepared and tested using a computercontrolled triaxial apparatus. The performed CDand CU tests are listed in table 2.

Drained Tests

According to table 2, fourteen CD tests wereperformed on the Kish Island, seven havingrelative density of %20 and 7 having relative

density of %80. Initial confining pressure wasselected from 50kPa to 600kPa. Six CD testswere performed on Tonbak sand having relativedensity of %20, with confining pressure from50kPa to 600kPa.

Diagram of B1/ B3 and volumetric strains againstaxial strain are shown in figures 3 and 4 for KishIsland sand in loose and dense state respectively.As shown in these figures, Kish Island sandshows a dilative behavior. In fact after acontraction portion, all samples are dilated.Dilation is more in dense state relative to loosestate. However, it seems that the Kish Island sandhas a substantial interlocking that even in loosestate shows a dilative behavior. As expected,increasing the initial confining pressure reduces


��

Fig.2 Microscopic electronic pictures of (a) Kish Island sand and (b) Tonbak sand.

sand Gs (min)d�(kN/m3)

(max)d�(kN/m3)

maxe mine minmax ee � CaCO3 (%)

Kish Island 2.68 15.6 17.8 0.72 0.51 0.21 93 Tonbak 2.69 13.4 15.6 0.99 0.71 0.28 95.5

Table 1 Physical Properties of Kish Island and Tonbak sand

the dilation.

However, the sand shows the contractionbehavior just in loose state and confiningpressure of 600kPa.

Almost, all samples show the volume increasingto strains up to %20. It means that, it’s not happenthe critical state to strains up to %20. Perhaps inthis soil, the critical state is achieved in strainsgreater than %20. Apparently, diagrams ofB1/ B3 against axial strains show the constant

shear strength just in confining pressure greaterthan 500kPa.

Diagrams of B1/ B3 and volume strains againstaxial strains are shown in figure 5 for Tonbaksand in loose state. As shown in this figure in lowconfining stresses, Tonbak sand has dilationbehavior. Increasing of confining pressure

reduces the dilation rate and samples show thecontraction behavior. Apparently, in this soil andhigh confining pressures, the critical state isclearer. Therefore, regarding to the structure ofthe two sands (figure 2); it can be said that 1) calcareous sands have substantially dilativebehavior due to inherent interlocking and 2) sands having weak structure have low dilationpotential. In other words, dilation and contractionresulted from particles breakage complexe thecritical state concept in these soils.

Comparing figures 3b and 5b, it is observed thatin low confining pressure (50kPa) the Kish Islandsand has low dilation in comparison with Tonbaksand. In high confining pressure (greater than500kPa) the dilation of Tonbak sand is omittedcompletely. Regarding the structure of the twosand grains, probably this behavior shows thatthe particles breakage of Tonbak sand is more


Sand Dr (%) Test 3� (kPa) Code Kish Island 20 CD 50 KL50CDKish Island 20 CD 100 KL100CDKish Island 20 CD 200 KL200CDKish Island 20 CD 300 KL300CDKish Island 20 CD 400 KL400CDKish Island 20 CD 500 KL500CDKish Island 20 CD 600 KL600CDKish Island 80 CD 50 KD50CDKish Island 80 CD 100 KD10CDKish Island 80 CD 200 KD200CDKish Island 80 CD 300 KL300CDKish Island 80 CD 400 KL400CDKish Island 80 CD 500 KL500CDKish Island 80 CD 600 KL600CDKish Island 20 CU 100 KL100CUKish Island 20 CU 300 KL300CUKish Island 20 CU 500 KL500CUKish Island 80 CU 100 KD100CUKish Island 80 CU 300 KD300CUKish Island 80 CU 500 KD500CU

Tonbak 20 CD 50 TL50CDTonbak 20 CD 100 TL100CDTonbak 20 CD 200 TL200CDTonbak 20 CD 300 TL300CDTonbak 20 CD 500 TL500CDTonbak 20 CD 600 TL600CDTonbak 20 CU 100 TL100CUTonbak 20 CU 300 TL300CUTonbak 20 CU 500 TL500CU

Table 2 The list of performed CD and CU tests


0

1

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3

4

5

6

0 5 10 15 20 25�1 (%)

� �' 1/��

' 3

KLCD50KLCD100KLCD200KLCD300KLCD400KLCD500KLCD600

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25

�1 (%)

�� v(%

)

KLCD50KLCD100KLCD200KLCD300KLCD400KLCD500KLCD600

��

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Fig. 3 Triaxial test results on Kish Island sand in loose state (a) B1/ B3 (b) volumetric strain against axial strain

0

1

2

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7

0 5 10 15 20 25�1 (%)

��' 1

/ ��' 3

KDCD50KDCD100KDCD200KDCD300KDCD400KDCD500KDCD600

-2

-1

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

�1 (%)

�� v (

%)

KDCD50KDCD100KDCD200KDCD300KDCD400KDCD500KDCD600

��

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Fig.4 Triaxial test results on Kish Island sand in dense state (a) B1/ B3 (b) volumetric strain against axial strain

0

1

2

3

4

5

6

7

0 5 10 15 20 25�1 (%)

� �' 1

/ � �' 3

TLCDT50TLCDT100TLCDT200TLCDT300TLCDT500TLCDT600

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20

�1 (%)

� � v (

%)

TLCUT50TLCUT100TLCUT200TLCUT300TLCUT500TLCUT600

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Fig.5 Triaxial test results on Tonbak sand in loose state (a) B1/ B3 (b) volumetric strain against axial strain

than Kish Island sand. It’s noted that particlesbreakage is accompanied with volume reduction.

Particle breakage and energy aspects

The Rowe stress- dilation theory in triaxial test isas:

(1)

Where B1 is the maximum principal stress, B3 isthe minimum principal stress, d v is thevolumetric strain increment (dilation positive),d 1 is the axial strain increment (compressionpositive) and is the internal friction anglebetween soil grains. Equation 1 has beenobtained based on the principle of minimum ratioof the rate of work done on the soil by B1 to thatdone by the soil against B3.

TZOU-SHIN UENG and TSE-JEN CHEN(2000) showed that if the soil grains crush duringloading in triaxial test, the Rowe’s equation ismodified as:

(2)

Where dEB is the energy consumed rate to grainscrushing.

Rowe based on experimental tests showed that in equation 1 should be replaced by f , that variesfrom in the maximum relative density to cv inthe loose interlocking and constant volumechange. This differences between f and is dueto the energy consumed during rearrangement ofsoil grains. Therefore, in this paper f is usedinstead of that f is the internal friction anglewithout considering the dilation and particlebreakage.

Considering the dilation and particles breakage ininternal friction angle (equation 1 withoutd v/d 1), results of CD tests are shown in figure 6as the total friction angle against initial confiningpressure. According to this figure, increasing theconfining pressure reduces the internal frictionangle. Furthermore, as it’s expected, increasingthe initial relative density increases the internalfriction angle (Kish Island sand). As shown infigure 6, it should be noted, although calcareoussands have shown some problems andweaknesses during constructions such as piledriving. It seems that they show a very suitablestrength using usual laboratory triaxial tests.However, the two investigated sands have similarmineralogy, but they show different strengths.Tonbak sand having brittle structure shows agreater internal friction angle in confiningpressure less than 300kPa and lower internalfriction angle in confining pressures higher than300kPa in comparison with Kish Island sand.


)2

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13

1 ��

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dd v

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45(tan)1(13

2

13

1�

� ��

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ddE

dd Bv

35

37

39

41

43

45

47

49

0 100 200 300 400 500 600

�3 (kPa)

�� (

deg

ree)

Kish, Dr=%20Kish, Dr=%80Tonbak, Dr=%20

-2

0

2

4

6

8

10

12

0 100 200 300 400 500 600

P (kPa)

�(d

e gre

es)


Fig.6 Total internal friction angle of Kish Islamd andTonbak sands against confining pressure

Fig.7 Dilation angle of Kish Island and Tonbak sandsagainst confining pressure

Dilation angle (differences between total frictionangle and the internal friction angle fromequation 1) of Kish Island sand in both loose anddense states and Tonbak sand is shown in figure7 against initial confining pressure. It’s observedthat calcareous sands have substantially aconsiderable dilation angle even in loose state.Increasing the confining pressure reduces thedilation angle. Beside this, regarding the brittlestructure of Tonbak sand grains, its dilation angleis lower than Kish Island sand especially in highconfining pressure. Tonbak sand in confiningpressure greater than 500kPa shows a negativedilation angle (contraction).

Consolidated-drained test results are shown infigure 8 as B1/ B3 against (1+d v/d 1). Accordingto Rowe’s theory, it is expected that the bestfitting line to the test results pass trough theorigin. However, this doesn’t occur. Comparingthe equation 2 and figure 8, it’s observed thatparticles breakage has apparently changed theshear strength envelop in the investigated sands.It is noted that the effect of particles breakage isdifferent in two studied sands. According tofigure 8 the shear strength envelops of the twoinvestigated sands are as:

(3)

Where the second terms show the effect ofparticles breakage and are different for the twosands.

It can be said that the consumed energyincrement (equation 2) to particle breakage is afunction of both the amount of breakage andcrushability potential or crushing strength ofgrains. Then, regarding to weaker structure, it’sexpected that Tonbak sand has greater grainscrushing. Considering that particles breakage isaccompanied by volume reduction, it reduces thedilation. The internal friction angle withoutdilation and particle breakage ( f in equation 2)is achieved using the experimental equationsobtained for the two sands (equation 3).Therefore, internal friction angles ( f ) of the twostudied sands are 32.6 and 33.4 for Kish Islandand Tonbak sand respectively. It’s clear that thedifference between these angles and the amountobtained from equation 2 are the particlesbreakage portion. Figure 9 shows the particlesbreakage portion from total internal friction angleagainst confining pressure. According to thisfigure, the particles breakage portion in loosesamples is greater than dense samples (KishIsland sand). It probably means the loose samplescrushability potential is greater than densesamples. Furthermore, particles breakage inTonbak sand is greater than Kish Island sand.Totally, unlike dilation, increasing the confining


y = 3.3601x + 0.8424R2 = 0.9921

y = 3.4426x + 1.0506R2 = 0.9974

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1

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3

4

5

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7

8

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1+d�v/d�1

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KishTonbakLinear (Kish)Linear (Tonbak)

Fig.8 Effect of particle breakage on the shear strengthenvelop of Kish Island and Tonbak sands

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600

P (kPa)

��(d

egre

e)


Fig.9 Particles breakage angle in the two studied sands

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pressure increases the particles breakage angle.Regarding that the analysis is performed in peakpoint, it is possible to calculate the consumedenergy to particles breakage by using theexperimental shear failure envelop (figure 8).Using this figure and equation 2 we have:

(4)

That b parameter is obtained by comparingequation 2 with figure 8. The b parameter is 0.84and 1.051 for Kish Island and Tonbak sandrespectively. The consumed energy for particlesbreakage to total applied energy on the sampleratio ( EB/ TT) in peak point is shown in figure10 against mean confining pressure (P). Asshown in this figure, increasing the confiningpressure and reducing the initial relative densityincreases the consumed energy to particlesbreakage (Kish Island sand). As expected, inTonbak sand having weaker structure, theconsumed energy to particles breakage is greaterthan Kish Island sand.

Grain size distribution

Grain size distribution of samples before andafter test is compared to evaluation of particles

breakage during consolidation and shearing.Considering particles breakage ratio definition(Br) according to figure 11, test results for thetwo studied sands are shown in figure 12. Due toparticles erosion effects in sieving, the obtainedgrading curves are accompanied by some errorsdespite similar method of grading the samples.As shown in figure 12, the particles breakage ofTonbak sand is greater than Kish Island sand.Also it is observed that increasing the confiningpressure and reducing the initial relative densityincreases the particle breakage ratio. It is clearthat the particles breakage of Tonbak sand isabout 5 to 6 times of Kish Island sand in similarconditions. However, the consumed energy toparticles breakage in Tonbak sand is less than 1.5times of Kish Island sand. Therefore, it can besaid that the consumed energy to particlesbreakage is a function of both the amount ofparticles breakage and particles breakagepotential or particles breakage strength. Particlestrength against breakage can be a function ofparticle hardness, shape and its internal porosity.Then Tonbak sand grains are experienced morecrushing regarding to weaker and brittlestructures.

Discussion

Coop (2004) performing ring shear tests on


5

7

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11

13

15

17

19

0 200 400 600 800 1000 1200 1400 1600P (kPa)

��E

B/ �

ET

Tonbak, Dr=%20Kish, Dr=%20Kish, Dr=%80

Fig.10 The consumed energy for particles breakage to totalapplied energy on samples ratio in peak point

∑

∑

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)(

)sin1/(

113

13

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f

EBET

bEB

Fig.11 definition of particle breakage ratio ( )100SABD

SABCBr


0

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0 5 10 15 20

�1 (%)

q (k

Pa)

KLCU100

KLCU300

KLCU500

0

400

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2000

0 200 400 600 800 1000 1200 1400

P' (kPa)

q (k

Pa)

KLCU100

KLCU300

KLCU500

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0 5 10 15 20�1 (%)

q (k

Pa)

KDCD100

KDCD300

KDCD500

0

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0 200 400 600 800 1000 1200 1400 1600

P' (kPa)

q (k

Pa)

KDCU100

KDCU300

KDCU500

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Fig.13 CU tests on Kish Island sand in loose and dense state: (a) q against axial strain, (b) q against P'

0

300

600

900

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1500

0 5 10 15 20 25

�1 (%)

q (k

Pa)

TLCUT100

TLCUT300

TLCUT500

0

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500

750

1000

1250

1500

0 100 200 300 400 500 600 700 800

P' (kPa)

q (k

Pa)

TLCUT100TLCUT300TLCUT500

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Fig.14 CU tests on Tonbak sand in loose state: (a) q against axial strain, (b) q against P'

0

4

8

12

16

20

24

0 200 400 600 800 1000 1200 1400 1600

P (kPa)

Br (%

)

Tonbak, Dr=%20Kish, Dr=%20Kish, Dr=%80

Fig.12 Particles breakage ratio of the two sand grains during CD tests

calcareous sands, presented that particlesbreakage is not only the function of normalstresses but it is also a function of experiencedshear strains. Regarding to limit strains in triaxialtests, it may not be to exactly simulate thephenomenon such as pile driving in calcareoussands. However, it may be to judge about otherstructures behavior such as shallow foundation orretaining walls. Considering simultaneousinteraction of dilation and particles breakage, thecritical state in triaxial tests is complex.According to the conducted triaxial tests on twodifferent calcareous sands, the apparent criticalstate is observed only in Tonbak sand andconfining pressures greater than 500kPa. Asstated before, this state is in fact a transient and abalance between dilation and volume reductionresulted from particles breakage. In the studiedsands and confining pressures less than 500kPa,it is not observed the critical state to strains up to%20. Regarding that the rate of volumeincreasing reduces by increasing the axial strains,it may be, the critical state is achieved in axialstrains greater than %20. The situation in whichdilation and particles breakage is ceased andconstant grading and relative density is achieved.Probably, the grain crushing is continued to verylarge strains after termination of dilation. If weaccept that such an event is happen during piledriving and the volume reduction is notcompensated by the lateral deflection of thearound soil, then the friction resistance fallsbetween the pile surface and soil (for example inloose and weakly cemented calcareous sands). Itmay be say that in these sands, the real criticalstate is a function of grains crushability, initialgrading, initial relative density and confiningpressure.

Undrained Tests

As listed in table 2, some CU triaxial tests wereperformed on Kish Island and Tonbak calcareoussands. Results of these tests are shown in figure13 as q against axial strain and P’ in both looseand dense states. According to figure 13a, it’sobserved that Kish Island dense samples haveapparently two yield points. One of them is in the

contraction or positive pore water pressuredevelopment zone and strains about %1. Anotheris in the dilation or negative pore water pressuredevelopment zone and strains about %(12-13).The mentioned behavior is weakly observed forloose samples. According to figure 13b, thenegative pore water pressure is developed after asmall contraction and positive pore waterpressure development. The difference of looseand dense samples is the amount of initialcontraction and secondary dilation. It means thatthe dense samples have shown greater negativepore water pressure in which results to highershear strength. However, it seems that the effectof inherent dilation is more efficient than theinitial relative density.

Test results on Tonbak sand are shown in figure14 as q against axial strain and P’ for loose state.Regarding figure 5, it is expected that this sandshows lower positive pore water pressureespecially in high confining pressures (figure 14).Considering of more brittle and weak structure ofTonbak sand grains, it’s experienced greaterparticles breakage. As mentioned before,particles breakage results in volume reductionand then development of positive pore waterpressure. Increasing the confining pressureincreases the particles breakage and volumereduction of samples. If the volume reductionresulted from particles breakage is greater thanthe inherent dilation, positive pore water pressureis developed. However, in Kish Island sand thevolume reduction resulted from particlesbreakage is less than the inherent dilation even toconfining pressure up to 500kPa. Therefore,considering continues negative pore waterpressure development especially in Kish Islandsand, the concept of critical state is complex inCU tests.

Conclusion

Based on drained and undrained triaxial tests ontwo calcareous sands obtained from Persian Gulfhaving different structures, it is observed that:- Calcareous sands have substantial interlockingthat result in dilative behavior of them in both


loose and dense state. May be the effect ofdilation greater than the effect of initial relativedensity. Increasing the confining pressuredecreases the dilation. Regarding the calcareoussoil structure, it may be, increasing the confiningpressure in the range of engineering stresses,dilation completely cease or exist.

- According to Rowe theory and its improvedversion for soils having crushable grains, somepart of applied energy to the sample during thetest is consumed to breakage of sand particles.Consumed energy to breakage of grains is afunction of both grains crushing strength andcrushing amount. Decreasing the relative densityand weakening the sand grains, increases theratio of consumed energy to breakage ofparticles.

- Internal friction angle in calcareous soils havingcrushable grains is formed from threecomponents: substantial friction of grains,dilation and grains breakage. Increasing theconfining pressure decreases the dilationcomponent and increases the breakagecomponent. Inherent dilation and crushing ofgrains result in complex the critical state concept.In fact, the critical state in calcareous soils havingthe mentioned two potential in triaxial tests is atransient state and a balance between dilation andcontraction due to particle breakage.

- Regarding that particles breakage is related toapplied strains and strain limitation of triaxialapparatus, prediction the derived piles bearingcapacity using usual triaxial test results is notexact.

Refference

Shambhu, S., Sharma and Mostafa A.,Ismail (2006). “Monotonic and CyclicBehavior of Two Calcareous Soils ofDifferent Origins”, J. Geotec. Eng. Div.,Am. Soc. Civ. Eng., 128(6), 20-529.

Coop, M.R., Sorensen, K. K., Bodas, T. &Georgoutsos G, (2004). “Particle breakageduring shearing of a carbonate sand.”.

Luzzani, L. and Coop, M. R. (2002). “Onthe relationship between particle breakageand citical sate of snds”, Soils andFoundation J. Vol. 42, No. 2, pp. 77-82.

Salehzadeh, M, (2000). “The behavior ofnon-cemented and artificially cementedcarbonate sand under monotonic andreversed cyclic shearing” Ph.D. Thesis,Univ. of Manchester, UK.

TZOU-SHIN UENG and TSE-JEN CHEN(2000). “Energy aspects of particlebreakage in drained shear os sands”,Geotechnique, 50(1), 65-72.

Ismail, M.A., Joer, H.A., Merit, A., andRandolph, M.F. (2002). “Cementation ofporous material using calcite”,Geotechnique, 52(5), 313-324.

Coop, M. R. (1999). “The influence on in-situ state on the behavior on carbonatesands.”, Proc., The Second InternationalConference on Engineering for CalcareousSediments, Bahrain, 21-24 February.

Carter, J.P., Airey, D.W. and Fahey, M.(1999). “A review of laboratory testing ofcalcareous soils”, Proc., The SecondInternational Conference on Engineeringfor Calcareous Sediments, Bahrain, 21-24February.

Coop, M.R. and Lee, I.K. (1993). “Thebehavior of granular soils at elevatedstresses.”, Predictive Soil Mechanics,Proc., C.P.Wroth Mem Symposium,Thomas Telford, London, 186-198.

Al- Shafei, K. A. (1999), Proc., 2nd Int.Conf. on Engineering for CalcareousSediments, Balkema, Rotterdam, TheNetherlands.

Baharom, B. and Stallebrass, S. E. (1998),“A constitutive model combining themicroscopic and macroscopic behavior ofsands in shear and volumetricdeformation”, Proc. 4th Eur. Conf. onNumerical Methods in Geotech. Engng.Udine, 1998, Springer-Verlag Wien, NewYork. 1998, 263-273.

Semple, R.M. (1988), “MechanicalProperties of Calcareous Soils: State of theArt Report”, Proc. of lst InternationalConference on Calcareous Sediments,


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Documents

Dilation and particle breakage effects on the shear